Our manuscript is divided into 7 sections. After this introduction in section  we summarize shortly the results on quantum dynamics of the bare Zwanzig model. It is discussed also a possible physical realization most closely satisfying the model assumptions. The section contains also an extended list of references to compensate partially its brevity.
Then in section  utilizing developed in our works [1]} - [2]} theoretical approach we investigate with all details the evolution of the population of the initially prepared single state of the system.
In section  we analyze various physically motivated generalizations of the bare Zwanzig model, and how our analytical
method should be modified to describe theoretically these generalizations. In the same section (subsection REF  we show that on similar footing we can study dynamics not only for an individual (single) nano-system but as well for the ensemble of somehow distributed nano-systems. We investigate the reservoir states evolution in section . We collect some already discussed in the literature and new applications of our approach to physically interesting phenomena in nano-systems. Namely, two-level systems coupled to reservoir (subsection REF ),
propagation of vibrational excitations in nano-size chains (subsection REF ).
The last section
 summarizes the main findings of our work, with a discussion of possible physical consequences and interpretation of the results.
